Problem: Simplify the following expression: $\sqrt{27}-\sqrt{48}+\sqrt{12}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{27}-\sqrt{48}+\sqrt{12}$ $= \sqrt{9 \cdot 3}-\sqrt{16 \cdot 3}+\sqrt{4 \cdot 3}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{3}-\sqrt{16} \cdot \sqrt{3}+\sqrt{4} \cdot \sqrt{3}$ $= 3\sqrt{3}-4\sqrt{3}+2\sqrt{3}$ Finally, simplify by combining the terms. $= ( 3 - 4 + 2 )\sqrt{3} = \sqrt{3}$